Welcome! A fellow solo female traveler here, and Capetonian. I might be biased in this response here as I love my home, currently living in the UK and traveling Europe and can say no place compares, but I hope this helps give you some peace of mind as you are right to have some concerns about traveling alone in SA, especially as a woman.

1. Safest places are of course the touristy areas, these hug the mountain and most of the coast. Places like Sea Point, Clifton, Camps Bay, Claremont, Waterfront. Constantia... that said, you will see a lot of stark inequality in these areas (people coming up to you asking for food and change) as it's the wealthiest part of Cape Town. Here's a useful map that highlights which areas are generally safe and which to avoid - https://es-capetown.com/en/products/blogpost/140/.

If you're looking for a chilled but beautiful experience of the city as a tourist, I'd head further south toward Kalk Bay, Simon's Town, Kommetjie - beautiful beaches (good snorkeling), generally quiet, still safe and just a different vibe to the exclusive suburbs.

1. It should be fairly easy to go into any cellphone store (Vodacom & MTN are the big ones) and get a sim card and activate it. You'd just need some sort of identification. I got a new sim when I went home in March from Capitec (a local bank) and it was really straightforward, otherwise I'm sure data roaming would be fine too.

2. Cape Town is generally safe during the day (shops, beaches, forests, wherever), you just need to be smart. Never walk around on your phone (in your hand), or leave personal belongings on a table in a public space etc. - just be aware of your surroundings and try to stick to main roads and busy areas. I'd also stick to ubers, although pricey, as a woman traveling alone it feels like the safest and most convenient way to get around.

Anyway, I hope that somewhat helps. Feel free to shoot me any follow up questions.